The Chrysler Corp. said yesterday that because of lagging auto sales it will run out of money sooner than expected and will need federal backing for an "interim" loan in January if the company is to stay afloat.

The disclosure, made to administration officials by company chairman Lee Iacocca, prompted a new appeal by the White House for Congress to pass the Chrysler loan-guarantee bill next week rather than postponing it to next session.

In a hastily called briefing, Vice President Mondale, stressing that he was speaking "on behalf of the president," said it was "essential that Congress act immediately . . . so that we can provide security for thousands . . . of jobs."

The Chrysler aid legislation is slated to come up for floor action in the House on Tuesday, with passage considered likely by Wednesday at the latest.However, the measure still has not been scheduled in the Senate.

Until yesterday, Iacocca and others had left the impression that the company would be able to sell enough cars to hold out through February, giving Congress a few Week's leeway if necessary to push the loan bill through.

However, Chrysler said yesterday that "current softness in the economy and in the car market are creating a cash drain at Chrysler, and interim funding will be necessary in January." Any such bridge loan will require federal backing.

The tightening in Chrysler's cashflow position was regarded as a significant, although not catastrophic, change in the company's financial outlook. However, in Chrysler's situation, even a small shift can make an important difference.

The glummer assessment of the company's financial posture, which followed a mid-month review on Thursday, was reported by Iacocca to Treasury Secretary G. William Miller late that evening. The two conferred again yesterday.

Officials said yesterday the administration was making the company's new position public in an effort to be sure Congress was aware of the new urgency in the situation and to head off any postponement of the bill to next session.

The loan guarantee legislation would provide $1.5 billion in federal backing, paving the way for some $3.3 billion to $4.2 billion in loans from banks, unions and other sources.